The Red Rose head coach had previously praised the 30-year-old fly-half for his attitude in training as he looked to secure a place in the XV during the three-Test tour.
Cipriani did make an appearance in last weekend's 23-12 defeat to end his three-year exile from the England side, and he will now replace George Ford in the starting line-up in Cape Town on Saturday as the side look to avoid a series whitewash against the Springboks.
"We are expecting a wet and windy old day at Newlands and have elected to play Danny Cipriani ahead of George Ford to give us a left-foot kicking option," said Jones.
Ford drops out of the 23-man squad for the game, while flanker Brad Shields is also absent out through illness, but Chris Robshaw is set to return.
Prop Joe Marler and number eight Nathan Hughes also start in place of the unavailable Mako Vunipola and his injured brother Billy.
"We've had a really upbeat training week," added Jones, looking ahead to the game. "We are up for the battle and are going to rip in on Saturday. We want another committed performance where it will be crucial to maintain our composure when the heat is on.
"I've been really impressed with the fortitude of the squad under Owen Farrell, who is a young captain, and with a number of young players who have really stuck to the task."